$B$ Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background (1801.07256v2)

Abstract: Lepton number as a fourth color is the intriguing theoretical idea of the famous Pati-Salam (PS) model. While in conventional PS models, the symmetry breaking scale and the mass of the resulting vector leptoquark are stringently constrained by $K_L\to\mu e$ and $K\to\pi\mu e$, the scale can be lowered to a few TeV by adding vector-like fermions. Furthermore, in this case, the intriguing hints for lepton flavour universality violation in $b\to s\mu^+\mu^-$ and $b\to c\tau\nu$ processes can be addressed. Such a setup is naturally achieved by implementing the PS gauge group in the five-dimensional Randall-Sundrum background. The PS symmetry is broken by boundary conditions on the fifth dimension and the resulting massive vector leptoquark automatically has the same mass scale as the vector-like fermions and all other resonances. We consider the phenomenology of this model in the context of the hints for lepton flavour universality violation in semileptonic $B$ decays. Assuming flavour alignment in the down sector we find that in $b\to s\ell^+\ell^-$ transitions the observed deviations from the SM predictions (including $R(K)$ and $R(K^*)$) can be explained with natural values for the free parameters of the model. Even though we find sizable effects in $R(D)$, $R(D^*)$ and $R(J/\Psi)$ one cannot account for the current central values in the constrained setup of our minimal model due to the stringent constraints from $D-\bar D$ mixing and $\tau\to 3\mu$.

• The paper introduces a novel approach by embedding the Pati-Salam model in a Randall-Sundrum background to address B meson decay anomalies.
• It uses vector-like fermions and boundary condition symmetry breaking to achieve reduced mass scales, aligning with LFU violation data.
• Numerical analyses identify viable parameter regions while noting challenges with observables like R(D), R(D*), and tau decay constraints.

Analyzing $B$ Meson Anomalies within the Pati-Salam Model and Randall-Sundrum Framework

The paper "B Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background" proposes an innovative approach to address certain anomalies in $B$ meson decays, particularly those suggesting lepton flavor universality (LFU) violation. Building on the Pati-Salam (PS) model with additional considerations in a five-dimensional Randall-Sundrum (RS) background, the paper addresses anomalies by hypothesizing reduced mass scales achievable through vector-like fermions.

Theoretical Framework

The Pati-Salam model, traditionally constrained by stringent decay processes such as $K_L\to\mu e$ and $K\to\pi\mu e$, sees potential for application with lowered symmetry breaking scales when vector-like fermions are introduced. This paper embeds the PS model into RS space-time, a maneuver allowing for scale reductions to a few TeV, circumventing typical constraints. The PS symmetry's breakdown is realized through boundary conditions applied to the fifth dimension, a compactification scheme that aligns the mass scale of the vector leptoquark (VLQ) with other resonances.

Phenomenological Considerations

Key to the research is examining the effects of the model on $B$ meson anomalies, specifically deviations in $b\to s\mu^+\mu^-$ and $b\to c\tau\nu$ transitions. The paper emphasizes flavor alignment in the down sector, demonstrating that natural free parameter values within the model account for the experimental discrepancies observed in these transitions. This theoretical setup achieves desirable alignment with the observed data on ratios such as $R(K)$ and $R(K^*)$, while incorporating minimal modifications to standard model (SM) assumptions.

One limitation identified within the paper is the inability of the model to account fully for central values of observables like $R(D)$ and $R(D^*)$ without violating constraints such as those imposed by $D-\bar D$ mixing. Additionally, the constraints on $\tau\to3\mu$ decays present further challenges to adjustment within this model framework.

Numerical and Experimental Analysis

The paper presents quantitatively plausible parameter regions for mass and interaction strengths that align with observed anomalies. For instance, when applying constraints from $b\to s\mu^+\mu^-$ transitions and the associated LFU violation indications, alongside mixing and decay parameters, subdivisions of parameter space that satisfy these constraints are illustrated. These regions reinforce the viability of this RS-PS model contingent on experimental bounds. Direct searches at the LHC impose a lower bound of approximately 3 TeV on resonance masses, consistent with other experimental searches such as dijet and $t\bar{t}$ resonance searches.

Implications and Further Research

The implications of this model are twofold: firstly, it proposes viable corrections for semileptonic $B$ decay anomalies under feasible parameter conditions; secondly, it invites further examination into the extension of PS models through extra dimensional theories. It poses potential avenues for addressing other anomalous observables, although refinements such as incorporating right-handed neutrinos or broader compositeness in the fermion sectors could extend the model's applicability. Future paper directions could also focus on assessing whether further deviations from standard symmetry assumptions might align additional measurable quantities such as the anomalous magnetic moment of the muon or directly observable rare decay rates.

Overall, this paper enriches the exploration of lepton flavor universality violations by leveraging a Pati-Salam model with Randall-Sundrum dimensional extensions, providing fertile ground for experimental and theoretical advancements in particle physics.